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A Measure of Comovement for Economic Variables: Theory and Empirics

TL;DR: In this article, a measure of dynamic comovement between (possibly many) time series and names it cohesion is defined in the frequency domain and is appropriate for processes that are costationary, possibly after suitable transformations.
Abstract: This paper proposes a measure of dynamic comovement between (possibly many) time series and names it cohesion. The measure is defined in the frequency domain and is appropriate for processes that are costationary, possibly after suitable transformations. In the bivariate case, the measure reduces to dynamic correlation and is related, but not equal, to the well known quantities of coherence and coherency. Dynamic correlation on a frequency band equals (static) correlation of bandpass-filtered series. Moreover, long-run correlation and cohesion relate in a simple way to co-integration. Cohesion is useful to study problems of business-cycle synchronization, to investigate short-run and long-run dynamic properties of multiple time series, and to identify dynamic clusters. We use state income data for the United States and GDP data for European nations to provide an empirical illustration that is focused on the geographical aspects of business-cycle fluctuations.

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Citations
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TL;DR: In this article, a suite of models, such as time-varying VAR techniques, traditional macro models, as well as DSGE models, were used to investigate the evolution of the link between inflation and resource utilization and its dependence on the nature and size of the shocks.
Abstract: A number of academic studies suggest that from the mid-1990s onwards there were changes in the link between inflation and economic activity. However, it remains unclear the extent to which this phenomenon can be ascribed to a change in the structural relationship between inflation and output, as opposed to a change in the size and nature of the shocks hitting the economy. This paper uses a suite of models, such as time-varying VAR techniques, traditional macro models, as well as DSGE models, to investigate, for various European countries as well as for the euro area, the evolution of the link between inflation and resource utilization and its dependence on the nature and size of the shocks. Our analysis suggests that the relationship between inflation and activity has indeed been changing over time, while remaining positive, with the correlation peaking during recessions. Quantitatively, the link between output and inflation is found to be highly dependent on which type of shocks hit the economy: while, in general, all demand shocks to output imply a reaction of inflation of the same sign, the latter will be less pronounced when output fluctuations are driven by supply shocks. In addition, a sharp deceleration of activity, as opposed to a subdued but protracted slowdown, results in a swifter decline in inflation. Inflation exhibits a rather strong persistence, with a negative impact still visible three years after the initial shock.

10 citations

Posted Content
TL;DR: In this article, an asymptotically consistent test, based on a subsampling approach, is presented to verify hypothesis about existence of the individual or common deterministic cycle in coordinates of multivariate macroeconomic time series.
Abstract: The aim of the article is to construct an asymptotically consistent test, based on a subsampling approach, to verify hypothesis about existence of the individual or common deterministic cycle in coordinates of multivariate macroeconomic time series. By the deterministic cycle we mean the periodic or almost periodic fluctuations in the mean function in cyclical fluctuations. To construct test we formulate a multivariate non-parametric model containing the business cycle component in the unconditional mean function. The construction relies on the Fourier representation of the unconditional expectation of the multivariate Almost Periodically Correlated time series and is related to fixed deterministic cycle presented in the literature. The analysis of the existence of common deterministic business cycles for selected European countries is presented based on monthly industrial production indexes. Our main findings from the empirical part is that the deterministic cycle can be strongly supported by the data and therefore should not be automatically neglected during analysis without justification.

10 citations

Journal ArticleDOI
TL;DR: In this article, the authors investigate the level of business cycles synchronisation between 8 Central and Eastern European Countries (CEEC) and the EU-15 using wavelet coherence and phase difference methodology.
Abstract: This paper strives to investigate the level of business cycles synchronisation between 8 Central and Eastern European Countries (CEEC) and the EU-15. We use wavelet coherence and phase difference methodology as a very suitable tool that observes simultaneously the strength of business cycles’ co-movement in the aspect of time as well as in the aspect of frequency. The results indicate that the business cycles of CEECs are generally synchronised with the EU-15 business cycles, whereas distinct differences existed before, during, and after the financial crisis (2008–2009) and during the European sovereign debt crisis (2010–2011). In other words, we demonstrate that very strong business cycles synchronisation occurred in almost all CEECs during crisis periods and at higher wavelet scales, while only moderate synchronisation is recorded in relatively tranquil periods at higher frequencies. The results suggest that smaller CEECs, but also larger countries such as the Czech Republic, Hungary, and to some extent Slovakia as well have a higher level of business cycles synchronisation with the EU-15, particularly in the crisis period at short-run as well as at long-run fluctuations. However, we do not find strong business cycles co-movement in cases of Poland and Latvia via HP and BP filters at higher frequencies during the crisis, which might indicate a higher resistance of these countries to external systemic shocks.

10 citations

Journal ArticleDOI
TL;DR: This paper examined the co-movement between Germany and South Africa by applying a dynamic factor model and concluded that a German supply shock has more of a demand-shock effect on the South African economy, while a German demand shock is transmitted through price in South Africa.
Abstract: This paper examines the co-movement between Germany and South Africa by applying a dynamic factor model. Because these two countries have a long history of predominant trade ties, they deemed to be suitable proxies to analyse the channels of transmission of positive supply and demand shocks in a developed economy and the effects of these on an emerging market economy. In contrast to general expectations, the paper concludes that a German supply shock has more of a demand-shock effect on the South African economy, while a German demand shock is transmitted through price in South Africa. This implies that the policy response in South Africa should not necessarily be the same as in Germany.

9 citations

Posted Content
TL;DR: In this article, the authors apply singular spectrum analysis (SSA) to the study of macroeconomic fluctuations in three European countries: Italy, The Netherlands, and the United Kingdom, and demonstrate its usefulness by analyzing several fundamental indicators of the three countries' real aggregate economy in a univariate, as well as a multivariate setting.
Abstract: The present work applies singular spectrum analysis (SSA) to the study of macroeconomic fluctuations in three European countries: Italy, The Netherlands, and the United Kingdom. This advanced spectral method provides valuable spatial and frequency information for multivariate data sets and goes far beyond the classical forms of time domain analysis. In particular, SSA enables us to identify dominant cycles that characterize the deterministic behavior of each time series separately, as well as their shared behavior. We demonstrate its usefulness by analyzing several fundamental indicators of the three countries' real aggregate economy in a univariate, as well as a multivariate setting. Since business cycles are international phenomena, which show common characteristics across countries, our aim is to uncover supranational behavior within the set of representative European economies selected herein. Finally, the analysis is extended to include several indicators from the U.S. economy, in order to examine its influence on the European economies under study and their interrelationships.

9 citations

References
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Journal ArticleDOI
TL;DR: The relationship between co-integration and error correction models, first suggested in Granger (1981), is here extended and used to develop estimation procedures, tests, and empirical examples.
Abstract: The relationship between co-integration and error correction models, first suggested in Granger (1981), is here extended and used to develop estimation procedures, tests, and empirical examples. If each element of a vector of time series x first achieves stationarity after differencing, but a linear combination a'x is already stationary, the time series x are said to be co-integrated with co-integrating vector a. There may be several such co-integrating vectors so that a becomes a matrix. Interpreting a'x,= 0 as a long run equilibrium, co-integration implies that deviations from equilibrium are stationary, with finite variance, even though the series themselves are nonstationary and have infinite variance. The paper presents a representation theorem based on Granger (1983), which connects the moving average, autoregressive, and error correction representations for co-integrated systems. A vector autoregression in differenced variables is incompatible with these representations. Estimation of these models is discussed and a simple but asymptotically efficient two-step estimator is proposed. Testing for co-integration combines the problems of unit root tests and tests with parameters unidentified under the null. Seven statistics are formulated and analyzed. The critical values of these statistics are calculated based on a Monte Carlo simulation. Using these critical values, the power properties of the tests are examined and one test procedure is recommended for application. In a series of examples it is found that consumption and income are co-integrated, wages and prices are not, short and long interest rates are, and nominal GNP is co-integrated with M2, but not M1, M3, or aggregate liquid assets.

27,170 citations

01 Jan 1987

3,983 citations


"A Measure of Comovement for Economi..." refers background in this paper

  • ...In this category belong the following three concepts: (i) the idea of co-integration (Engle & Granger, 1987): two processes are co-integrated if the spectral density at frequency zero has rank one; (ii) codependence (Gourieroux & Peaucelle, 1992), which refers to linear combinations of correlated…...

    [...]

Journal ArticleDOI
TL;DR: In this article, the authors present evidence that most of the unemployment fluctuations of the seventies (unlike those in the sixties) were induced by unusual structural shifts within the U.S. economy.
Abstract: A substantial fraction of cyclical unemployment is better characterized as fluctuations of the "frictional" or "natural" rate than as deviations from some relatively stable natural rate. Shifts of employment demand between sectors of the economy necessitate continuous labor reallocation. Since it takes time for workers to find new jobs, some unemployment is unavoidable. This paper presents evidence that most of the unemployment fluctuations of the seventies (unlike those in the sixties) were induced by unusual structural shifts within the U.S. economy. Simple time-series models of layoffs and unemployment are constructed that include a measure of structural shifts within the labor market. These models are estimated and a derived natural rate series is constructed.

1,128 citations

ReportDOI
TL;DR: In this paper, the authors introduce a class of statistical tests for the hypothesis that some feature that is present in each of several variables is common to them, which are data properties such as serial correlation, trends, seasonality, heteroscedasticity, auto-regression, and excess kurtosis.
Abstract: This article introduces a class of statistical tests for the hypothesis that some feature that is present in each of several variables is common to them. Features are data properties such as serial correlation, trends, seasonality, heteroscedasticity, autoregressive conditional hetero-scedasticity, and excess kurtosis. A feature is detected by a hypothesis test taking no feature as the null, and a common feature is detected by a test that finds linear combinations of variables with no feature. Often, an exact asymptotic critical value can be obtained that is simply a test of overidentifying restrictions in an instrumental variable regression. This article tests for a common international business cycle.

550 citations

Posted Content
TL;DR: The existence of a serial correlation common feature among the first differences of a set of I(1) variables implies the existence of common cycle in the Beveridge-Nelson-Stock-Watson decomposition of those variables as mentioned in this paper.
Abstract: The existence of a serial correlation common feature among the first differences of a set of I(1) variables implies the existence of a common cycle in the Beveridge-Nelson-Stock-Watson decomposition of those variables. A test for the existence of common cycles among cointegrated variables is developed. The test is used to examine the validity of the common trend-common cycle structure implied by Flavin's excess sensitivity hypothesis and Campbell and Mankiw's mixture of rational expectations and rule-of-thumb hypothesis for consumption and income. Linear independence between the cointegration and the cofeature vectors is exploited to decompose consumption and income into their trend and cycle components. Copyright 1993 by John Wiley & Sons, Ltd.

511 citations